Question: The equation of an ellipse $E$ is $\dfrac {(y+5)^{2}}{25}+\dfrac {(x-5)^{2}}{81} = 1$. What are its center $(h, k)$ and its major and minor radius?
Answer: The equation of an ellipse with center $(h, k)$ is $ \dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1$ We can rewrite the given equation as $\dfrac{(x - 5)^2}{81} + \dfrac{(y - (-5))^2}{25} = 1 $ Thus, the center $(h, k) = (5, -5)$ $81$ is bigger than $25$ so the major radius is $\sqrt{81} = 9$ and the minor radius is $\sqrt{25} = 5$.